Question: Solve for $x$ and $y$ using elimination. ${-2x+3y = 26}$ ${-3x+4y = 34}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $3$ ${8x-12y = -104}$ $-9x+12y = 102$ Add the top and bottom equations together. $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-2x+3y = 26}\thinspace$ to find $y$ ${-2}{(2)}{ + 3y = 26}$ $-4+3y = 26$ $-4{+4} + 3y = 26{+4}$ $3y = 30$ $\dfrac{3y}{{3}} = \dfrac{30}{{3}}$ ${y = 10}$ You can also plug ${x = 2}$ into $\thinspace {-3x+4y = 34}\thinspace$ and get the same answer for $y$ : ${-3}{(2)}{ + 4y = 34}$ ${y = 10}$